Critical Assessment on the Stability and Convergence of the Conventional Gear Tooth Contact Analysis

Maksat Temirkhan; Andas Amrin; Christos Spitas; Bakytzhan Sariyev; Chingis Kharmyssov

doi:10.46604/peti.2024.14062

Authors

Maksat Temirkhan Science Department, Astana IT University, Astana, Kazakhstan https://orcid.org/0000-0001-6283-3401
Andas Amrin Department of Mechanical and Aerospace Engineering, Nazarbayev University, Astana, Kazakhstan
Christos Spitas School of Aerospace Engineering, Department of Mechanical, Materials and Manufacturing Engineering, University of Nottingham, Ningbo, China
Bakytzhan Sariyev Science Department, Astana IT University, Astana, Kazakhstan
Chingis Kharmyssov Department of Physics, Zhetysu University, Taldykorgan, Kazakhstan

DOI:

https://doi.org/10.46604/peti.2024.14062

Keywords:

gear TCA, convergences issue, misalignments, spur gear, helical gear

Abstract

Mathematical modeling of gear engagement is crucial during design to ensure optimal performance in manufacturing. This study reproduces the conventional tooth contact analysis (TCA) model, highlighting convergence issues in parallel-axis gears and limitations in local synthesis methods. The research critically analyzes the TCA method, which solves five nonlinear equations to assess performance and accuracy. Simulations replicate the conditions of previous studies to ensure valid comparisons. Initial guess values are randomly generated within a specific range to guide the iterative process toward convergence, with this range progressively narrowed to improve computational efficiency and accuracy. Results indicate that the TCA approach is highly sensitive to initial guess values, particularly the starting angular position. Convergence issues arise from the complexity of nonlinear equations and multiple roots. This can lead to divergence or reverting to the initial guess when values deviate significantly from the true solution.

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